Strong completeness for a class of stochastic differential equations with irregular coefficients

We prove the strong completeness for a class of non-degenerate SDEs, whose coefficients are not necessarily uniformly elliptic nor locally Lipschitz continuous nor bounded. Moreover, for each $t$, the solution flow $F_t$ is weakly differentiable and for each $p>0$ there is a positive number $T(p)$ such that for all $t<T(p)$, the solution flow $F_t(\cdot)$ belongs to the Sobolev space W_{\loc}^{1,p}. The main tool for this is the approximation of the associated derivative flow equations. As an application a differential formula is also obtained

Dyson-Schwinger Equations with a Parameterized Metric

We construct and solve the Dyson-Schwinger equation (DSE) of quark propagator with a parameterized metric, which connects the Euclidean metric with the Minkowskian one. We show, in some models, the Minkowskian vacuum is different from the Euclidean vacuum. The usual analytic continuation of Green function does not make sense in these cases. While with the algorithm we proposed and the quark-gluon vertex ansatz which preserves the Ward-Takahashi identity, the vacuum keeps being unchanged in the evolution of the metric. In this case, analytic continuation becomes meaningful and can be fully carried out.Comment: 10 pages, 7 figures. To appear in Physical Review

Four new species of the genus Eurytenes Foerster (Hymenoptera: Braconidae: Opiinae) from China

The species of Eurytenes Foerster in China are revised and four new species are described fromChina: E. basinervis sp. n., E. glabratus sp. n., E. setoputeus sp. n. and E. rugosulcus sp. n. This genus is recorded from China for the first time

Effects of tidally enhanced stellar wind on the horizontal branch morphology of globular clusters

Metallicity is the first parameter to influence the horizontal branch (HB) morphology of globular clusters (GCs). It has been found, however, that some other parameters may also play an important role in affecting the morphology. While the nature of these important parameters remains unclear, they are believed to be likely correlated with wind mass-loss of red giants, since this mass loss determines their subsequent locations on the HB. Unfortunately, the mass loss during the red giant stages of the stellar evolution is poorly understood at present. The stellar winds of red giants may be tidally enhanced by companion stars if they are in binary systems. We investigate evolutionary consequences of red giants in binaries by including tidally enhanced stellar winds, and examine the effects on the HB morphology of GCs. We find that red, blue, and extreme horizontal branch stars are all produced under the effects of tidally enhanced stellar wind without any additional assumptions on the mass-loss dispersion. Furthermore, the horizontal branch morphology is found to be insensitive to the tidal enhancement parameter, Bw. We compare our theoretical results with the observed horizontal branch morphology of globular cluster NGC 2808, and find that the basic morphology of the horizontal branch can be well reproduced. The number of blue horizontal branch stars in our calculations, however, is lower than that of NGC 2808.Comment: 7 pages, 4 figures, 2 tables, accepted for publication in Astronomy & Astrophysic

Phase diagram and critical endpoint for strongly-interacting quarks

We introduce a method based on the chiral susceptibility, which enables one to draw a phase diagram in the chemical-potential/temperature plane for strongly-interacting quarks whose interactions are described by any reasonable gap equation, even if the diagrammatic content of the quark-gluon vertex is unknown. We locate a critical endpoint (CEP) at (\mu^E,T^E) ~ (1.0,0.9)T_c, where T_c is the critical temperature for chiral symmetry restoration at \mu=0; and find that a domain of phase coexistence opens at the CEP whose area increases as a confinement length-scale grows.Comment: 4 pages, 3 figure

Clinical observation of treatment of fungal corneal ulcer with application of iodine tincture and fluconazole

AIM: To explore the effect of 30g/L iodine rubbed and debridement of wound together with 2g/L fluconazole in the treatment of fungal corneal ulcers. <p>METHODS: Fifty fungal keratitis cases(50 eyes)diagnosed by corneal smear examination were cleaned locally, iodine blanch. All patients were given 2g/L fluconazole for systemic treatment, treated eye with 2g/L fluconazole eye-drops and loxacin eye-drops, and 30g/L atropine eye ointment dilate the pupils.<p>RESULTS:Fifty cases(50 eyes)were selected, of which, 40 cases were healed, 8 cases were improved and 2 cases were aggravated with operation being given.<p>CONCLUSION:After early and timely diagnosis of fungal keratitis, local debridement, 30g/L iodine rubbed the wound and joint with systemic and local treatment of fluconazole can achieve good effect

Superplastic Alumina Ceramics with Grain Growth Inhibitors

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65476/1/j.1151-2916.1991.tb06935.x.pd

Improved Decoding of Expander Codes

We study the classical expander codes, introduced by Sipser and Spielman [M. Sipser and D. A. Spielman, 1996]. Given any constants 0 < ?, ? < 1/2, and an arbitrary bipartite graph with N vertices on the left, M < N vertices on the right, and left degree D such that any left subset S of size at most ? N has at least (1-?)|S|D neighbors, we show that the corresponding linear code given by parity checks on the right has distance at least roughly {? N}/{2 ?}. This is strictly better than the best known previous result of 2(1-?) ? N [Madhu Sudan, 2000; Viderman, 2013] whenever ? < 1/2, and improves the previous result significantly when ? is small. Furthermore, we show that this distance is tight in general, thus providing a complete characterization of the distance of general expander codes. Next, we provide several efficient decoding algorithms, which vastly improve previous results in terms of the fraction of errors corrected, whenever ? < 1/4. Finally, we also give a bound on the list-decoding radius of general expander codes, which beats the classical Johnson bound in certain situations (e.g., when the graph is almost regular and the code has a high rate). Our techniques exploit novel combinatorial properties of bipartite expander graphs. In particular, we establish a new size-expansion tradeoff, which may be of independent interests